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<h1>src/qvsfm/qvgea/so3EssentialEvaluation.cpp</h1><a href="so3EssentialEvaluation_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/*</span>
<a name="l00002"></a>00002 <span class="comment"> *      Copyright (C) 2011, 2012. PARP Research Group.</span>
<a name="l00003"></a>00003 <span class="comment"> *      &lt;http://perception.inf.um.es&gt;</span>
<a name="l00004"></a>00004 <span class="comment"> *      University of Murcia, Spain.</span>
<a name="l00005"></a>00005 <span class="comment"> *</span>
<a name="l00006"></a>00006 <span class="comment"> *      This file is part of the QVision library.</span>
<a name="l00007"></a>00007 <span class="comment"> *</span>
<a name="l00008"></a>00008 <span class="comment"> *      QVision is free software: you can redistribute it and/or modify</span>
<a name="l00009"></a>00009 <span class="comment"> *      it under the terms of the GNU Lesser General Public License as</span>
<a name="l00010"></a>00010 <span class="comment"> *      published by the Free Software Foundation, version 3 of the License.</span>
<a name="l00011"></a>00011 <span class="comment"> *</span>
<a name="l00012"></a>00012 <span class="comment"> *      QVision is distributed in the hope that it will be useful,</span>
<a name="l00013"></a>00013 <span class="comment"> *      but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
<a name="l00014"></a>00014 <span class="comment"> *      MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span>
<a name="l00015"></a>00015 <span class="comment"> *      GNU Lesser General Public License for more details.</span>
<a name="l00016"></a>00016 <span class="comment"> *</span>
<a name="l00017"></a>00017 <span class="comment"> *      You should have received a copy of the GNU Lesser General Public</span>
<a name="l00018"></a>00018 <span class="comment"> *      License along with QVision. If not, see &lt;http://www.gnu.org/licenses/&gt;.</span>
<a name="l00019"></a>00019 <span class="comment"> */</span>
<a name="l00020"></a>00020 
<a name="l00024"></a>00024 
<a name="l00025"></a>00025 <span class="preprocessor">#include &lt;<a class="code" href="so3EssentialEvaluation_8h.html" title="File from the QVision library.">qvsfm/qvgea/so3EssentialEvaluation.h</a>&gt;</span>
<a name="l00026"></a>00026 <span class="comment">/*</span>
<a name="l00027"></a>00027 <span class="comment">Maple code to generate the function &#39;essentialEvaluation&#39;:</span>
<a name="l00028"></a>00028 <span class="comment">--------------------------------------</span>
<a name="l00029"></a>00029 <span class="comment"></span>
<a name="l00030"></a>00030 <span class="comment">###################</span>
<a name="l00031"></a>00031 <span class="comment"># Including modules with required functionality</span>
<a name="l00032"></a>00032 <span class="comment">#</span>
<a name="l00033"></a>00033 <span class="comment">with(VectorCalculus):</span>
<a name="l00034"></a>00034 <span class="comment">with(LinearAlgebra):</span>
<a name="l00035"></a>00035 <span class="comment"></span>
<a name="l00036"></a>00036 <span class="comment">###################</span>
<a name="l00037"></a>00037 <span class="comment"># Defining some projective algebra functions</span>
<a name="l00038"></a>00038 <span class="comment">#</span>
<a name="l00039"></a>00039 <span class="comment">Norm2 := V -&gt; sqrt(V(1)^2 + V(2)^2 + V(3)^2):</span>
<a name="l00040"></a>00040 <span class="comment">CrossProductMatrix := V -&gt; Matrix([[0, -V(3), V(2)], [V(3), 0, -V(1)], [-V(2), V(1), 0]]):</span>
<a name="l00041"></a>00041 <span class="comment"></span>
<a name="l00042"></a>00042 <span class="comment"># R =   cos(v_t)*I +</span>
<a name="l00043"></a>00043 <span class="comment">#       (sin(v_t)/v_t) * v.crossProductMatrix() +</span>
<a name="l00044"></a>00044 <span class="comment">#       ((1-cos(v_t))/ (v_t * v_t) )* v.toColumnMatrix() * v.toRowMatrix();</span>
<a name="l00045"></a>00045 <span class="comment">I3 := Matrix([[1,0,0],[0,1,0],[0,0,1]]):</span>
<a name="l00046"></a>00046 <span class="comment">Ang := V -&gt; Norm2(V) + Epsi:</span>
<a name="l00047"></a>00047 <span class="comment">expSO3 := V -&gt; cos(Ang(V)).I3 + (sin(Ang(V))/Ang(V)) . CrossProductMatrix(V) + (1-cos(Ang(V)))/(Ang(V) Ang(V)) . V . Transpose(V):</span>
<a name="l00048"></a>00048 <span class="comment"></span>
<a name="l00049"></a>00049 <span class="comment">###################</span>
<a name="l00050"></a>00050 <span class="comment"># Epipolar expression.</span>
<a name="l00051"></a>00051 <span class="comment">#</span>
<a name="l00052"></a>00052 <span class="comment"># The essential matrix is expressed related to two cameras, defined by the vectors</span>
<a name="l00053"></a>00053 <span class="comment">#</span>
<a name="l00054"></a>00054 <span class="comment">#       [v1x0, v1x1, v1x2, v1x3, v1x4, v1x5]</span>
<a name="l00055"></a>00055 <span class="comment">#</span>
<a name="l00056"></a>00056 <span class="comment">#       and</span>
<a name="l00057"></a>00057 <span class="comment">#</span>
<a name="l00058"></a>00058 <span class="comment">#       [v2x0, v2x1, v2x2, v2x3, v2x4, v2x5]</span>
<a name="l00059"></a>00059 <span class="comment">#</span>
<a name="l00060"></a>00060 <span class="comment">R1 := expSO3(Vector([v1x0, v1x1, v1x2])):</span>
<a name="l00061"></a>00061 <span class="comment">R2 := expSO3(Vector([v2x0, v2x1, v2x2])):</span>
<a name="l00062"></a>00062 <span class="comment">c1 := Vector([v1x3, v1x4, v1x5]):</span>
<a name="l00063"></a>00063 <span class="comment">c2 := Vector([v2x3, v2x4, v2x5]):</span>
<a name="l00064"></a>00064 <span class="comment">E := R2.CrossProductMatrix( (c2-c1) / Norm2(c2-c1)).Transpose(R1):</span>
<a name="l00065"></a>00065 <span class="comment"></span>
<a name="l00066"></a>00066 <span class="comment">###################</span>
<a name="l00067"></a>00067 <span class="comment"># Vectorized expression of the essential matrix</span>
<a name="l00068"></a>00068 <span class="comment">#</span>
<a name="l00069"></a>00069 <span class="comment">vectorE := Vector([E(1,1), E(1,2), E(1,3), E(2,1), E(2,2), E(2,3), E(3,1), E(3,2), E(3,3)]):</span>
<a name="l00070"></a>00070 <span class="comment"></span>
<a name="l00071"></a>00071 <span class="comment">###################</span>
<a name="l00072"></a>00072 <span class="comment"># Epipolar evaluation and Jacobian matrices.</span>
<a name="l00073"></a>00073 <span class="comment"># This matrix contains the jacobians for each pair of cameras in the map,</span>
<a name="l00074"></a>00074 <span class="comment"># and the evaluation of the epipolar error function, for the cameras</span>
<a name="l00075"></a>00075 <span class="comment">#</span>
<a name="l00076"></a>00076 <span class="comment">M := Matrix([</span>
<a name="l00077"></a>00077 <span class="comment">[ diff(vectorE(1), v1x0), diff(vectorE(1), v1x1), diff(vectorE(1), v1x2), diff(vectorE(1), v1x3), diff(vectorE(1), v1x4), diff(vectorE(1), v1x5), diff(vectorE(1), v2x0), diff(vectorE(1), v2x1), diff(vectorE(1), v2x2), diff(vectorE(1), v2x3), diff(vectorE(1), v2x4), diff(vectorE(1), v2x5), vectorE(1) ],</span>
<a name="l00078"></a>00078 <span class="comment">[ diff(vectorE(2), v1x0), diff(vectorE(2), v1x1), diff(vectorE(2), v1x2), diff(vectorE(2), v1x3), diff(vectorE(2), v1x4), diff(vectorE(2), v1x5), diff(vectorE(2), v2x0), diff(vectorE(2), v2x1), diff(vectorE(2), v2x2), diff(vectorE(2), v2x3), diff(vectorE(2), v2x4), diff(vectorE(2), v2x5), vectorE(2) ],</span>
<a name="l00079"></a>00079 <span class="comment">[ diff(vectorE(3), v1x0), diff(vectorE(3), v1x1), diff(vectorE(3), v1x2), diff(vectorE(3), v1x3), diff(vectorE(3), v1x4), diff(vectorE(3), v1x5), diff(vectorE(3), v2x0), diff(vectorE(3), v2x1), diff(vectorE(3), v2x2), diff(vectorE(3), v2x3), diff(vectorE(3), v2x4), diff(vectorE(3), v2x5), vectorE(3) ],</span>
<a name="l00080"></a>00080 <span class="comment">[ diff(vectorE(4), v1x0), diff(vectorE(4), v1x1), diff(vectorE(4), v1x2), diff(vectorE(4), v1x3), diff(vectorE(4), v1x4), diff(vectorE(4), v1x5), diff(vectorE(4), v2x0), diff(vectorE(4), v2x1), diff(vectorE(4), v2x2), diff(vectorE(4), v2x3), diff(vectorE(4), v2x4), diff(vectorE(4), v2x5), vectorE(4) ],</span>
<a name="l00081"></a>00081 <span class="comment">[ diff(vectorE(5), v1x0), diff(vectorE(5), v1x1), diff(vectorE(5), v1x2), diff(vectorE(5), v1x3), diff(vectorE(5), v1x4), diff(vectorE(5), v1x5), diff(vectorE(5), v2x0), diff(vectorE(5), v2x1), diff(vectorE(5), v2x2), diff(vectorE(5), v2x3), diff(vectorE(5), v2x4), diff(vectorE(5), v2x5), vectorE(5) ],</span>
<a name="l00082"></a>00082 <span class="comment">[ diff(vectorE(6), v1x0), diff(vectorE(6), v1x1), diff(vectorE(6), v1x2), diff(vectorE(6), v1x3), diff(vectorE(6), v1x4), diff(vectorE(6), v1x5), diff(vectorE(6), v2x0), diff(vectorE(6), v2x1), diff(vectorE(6), v2x2), diff(vectorE(6), v2x3), diff(vectorE(6), v2x4), diff(vectorE(6), v2x5), vectorE(6) ],</span>
<a name="l00083"></a>00083 <span class="comment">[ diff(vectorE(7), v1x0), diff(vectorE(7), v1x1), diff(vectorE(7), v1x2), diff(vectorE(7), v1x3), diff(vectorE(7), v1x4), diff(vectorE(7), v1x5), diff(vectorE(7), v2x0), diff(vectorE(7), v2x1), diff(vectorE(7), v2x2), diff(vectorE(7), v2x3), diff(vectorE(7), v2x4), diff(vectorE(7), v2x5), vectorE(7) ],</span>
<a name="l00084"></a>00084 <span class="comment">[ diff(vectorE(8), v1x0), diff(vectorE(8), v1x1), diff(vectorE(8), v1x2), diff(vectorE(8), v1x3), diff(vectorE(8), v1x4), diff(vectorE(8), v1x5), diff(vectorE(8), v2x0), diff(vectorE(8), v2x1), diff(vectorE(8), v2x2), diff(vectorE(8), v2x3), diff(vectorE(8), v2x4), diff(vectorE(8), v2x5), vectorE(8) ],</span>
<a name="l00085"></a>00085 <span class="comment">[ diff(vectorE(9), v1x0), diff(vectorE(9), v1x1), diff(vectorE(9), v1x2), diff(vectorE(9), v1x3), diff(vectorE(9), v1x4), diff(vectorE(9), v1x5), diff(vectorE(9), v2x0), diff(vectorE(9), v2x1), diff(vectorE(9), v2x2), diff(vectorE(9), v2x3), diff(vectorE(9), v2x4), diff(vectorE(9), v2x5), vectorE(9) ]</span>
<a name="l00086"></a>00086 <span class="comment">]):</span>
<a name="l00087"></a>00087 <span class="comment"></span>
<a name="l00088"></a>00088 <span class="comment">###################</span>
<a name="l00089"></a>00089 <span class="comment"># Display the C code to evaluate the previous matrix</span>
<a name="l00090"></a>00090 <span class="comment">#</span>
<a name="l00091"></a>00091 <span class="comment">CodeGeneration[C](M, optimize = true);</span>
<a name="l00092"></a>00092 <span class="comment"></span>
<a name="l00093"></a>00093 <span class="comment">*/</span>
<a name="l00094"></a>00094 
<a name="l00095"></a>00095 <span class="keywordtype">void</span> so3EssentialEvaluation(<span class="keyword">const</span> <span class="keywordtype">double</span> *pose1, <span class="keyword">const</span> <span class="keywordtype">double</span> *pose2, <span class="keywordtype">double</span> *cg0, <span class="keyword">const</span> <span class="keywordtype">double</span> Epsi)
<a name="l00096"></a>00096 {
<a name="l00097"></a>00097 <span class="keyword">const</span> <span class="keywordtype">double</span>
<a name="l00098"></a>00098         v1x0 = pose1[0],
<a name="l00099"></a>00099         v1x1 = pose1[1],
<a name="l00100"></a>00100         v1x2 = pose1[2],
<a name="l00101"></a>00101         v1x3 = pose1[3],
<a name="l00102"></a>00102         v1x4 = pose1[4],
<a name="l00103"></a>00103         v1x5 = pose1[5];
<a name="l00104"></a>00104 
<a name="l00105"></a>00105 <span class="keyword">const</span> <span class="keywordtype">double</span>
<a name="l00106"></a>00106         v2x0 = pose2[0],
<a name="l00107"></a>00107         v2x1 = pose2[1],
<a name="l00108"></a>00108         v2x2 = pose2[2],
<a name="l00109"></a>00109         v2x3 = pose2[3],
<a name="l00110"></a>00110         v2x4 = pose2[4],
<a name="l00111"></a>00111         v2x5 = pose2[5];
<a name="l00112"></a>00112 
<a name="l00113"></a>00113     <span class="keyword">const</span> <span class="keywordtype">double</span> t1 = v2x0 * v2x0;
<a name="l00114"></a>00114     <span class="keyword">const</span> <span class="keywordtype">double</span> t2 = v2x1 * v2x1;
<a name="l00115"></a>00115     <span class="keyword">const</span> <span class="keywordtype">double</span> t3 = v2x2 * v2x2;
<a name="l00116"></a>00116     <span class="keyword">const</span> <span class="keywordtype">double</span> t5 = sqrt(t1 + t2 + t3);
<a name="l00117"></a>00117     <span class="keyword">const</span> <span class="keywordtype">double</span> t6 = t5 + Epsi;
<a name="l00118"></a>00118     <span class="keyword">const</span> <span class="keywordtype">double</span> t7 = sin(t6);
<a name="l00119"></a>00119     <span class="keyword">const</span> <span class="keywordtype">double</span> t8 = 0.1e1 / t6;
<a name="l00120"></a>00120     <span class="keyword">const</span> <span class="keywordtype">double</span> t9 = t7 * t8;
<a name="l00121"></a>00121     <span class="keyword">const</span> <span class="keywordtype">double</span> t10 = t9 * v2x2;
<a name="l00122"></a>00122     <span class="keyword">const</span> <span class="keywordtype">double</span> t11 = cos(t6);
<a name="l00123"></a>00123     <span class="keyword">const</span> <span class="keywordtype">double</span> t12 = 0.1e1 - t11;
<a name="l00124"></a>00124     <span class="keyword">const</span> <span class="keywordtype">double</span> t13 = t6 * t6;
<a name="l00125"></a>00125     <span class="keyword">const</span> <span class="keywordtype">double</span> t14 = 0.1e1 / t13;
<a name="l00126"></a>00126     <span class="keyword">const</span> <span class="keywordtype">double</span> t15 = t12 * t14;
<a name="l00127"></a>00127     <span class="keyword">const</span> <span class="keywordtype">double</span> t17 = t15 * v2x0 * v2x1;
<a name="l00128"></a>00128     <span class="keyword">const</span> <span class="keywordtype">double</span> t18 = -t10 + t17;
<a name="l00129"></a>00129     <span class="keyword">const</span> <span class="keywordtype">double</span> t19 = (v2x3 * v2x3);
<a name="l00130"></a>00130     <span class="keyword">const</span> <span class="keywordtype">double</span> t22 = (v1x3 * v1x3);
<a name="l00131"></a>00131     <span class="keyword">const</span> <span class="keywordtype">double</span> t23 = (v2x4 * v2x4);
<a name="l00132"></a>00132     <span class="keyword">const</span> <span class="keywordtype">double</span> t26 = (v1x4 * v1x4);
<a name="l00133"></a>00133     <span class="keyword">const</span> <span class="keywordtype">double</span> t27 = (v2x5 * v2x5);
<a name="l00134"></a>00134     <span class="keyword">const</span> <span class="keywordtype">double</span> t30 = (v1x5 * v1x5);
<a name="l00135"></a>00135     <span class="keyword">const</span> <span class="keywordtype">double</span> t31 = t19 - 2 * v2x3 * v1x3 + t22 + t23 - 2 * v2x4 * v1x4 + t26 + t27 - 2 * v2x5 * v1x5 + t30;
<a name="l00136"></a>00136     <span class="keyword">const</span> <span class="keywordtype">double</span> t32 = sqrt(t31);
<a name="l00137"></a>00137     <span class="keyword">const</span> <span class="keywordtype">double</span> t33 = 0.1e1 / t32;
<a name="l00138"></a>00138     <span class="keyword">const</span> <span class="keywordtype">double</span> t34 = t18 * t33;
<a name="l00139"></a>00139     <span class="keyword">const</span> <span class="keywordtype">double</span> t35 = v2x5 - v1x5;
<a name="l00140"></a>00140     <span class="keyword">const</span> <span class="keywordtype">double</span> t37 = t9 * v2x1;
<a name="l00141"></a>00141     <span class="keyword">const</span> <span class="keywordtype">double</span> t39 = t15 * v2x0 * v2x2;
<a name="l00142"></a>00142     <span class="keyword">const</span> <span class="keywordtype">double</span> t40 = t37 + t39;
<a name="l00143"></a>00143     <span class="keyword">const</span> <span class="keywordtype">double</span> t41 = t40 * t33;
<a name="l00144"></a>00144     <span class="keyword">const</span> <span class="keywordtype">double</span> t42 = v2x4 - v1x4;
<a name="l00145"></a>00145     <span class="keyword">const</span> <span class="keywordtype">double</span> t44 = t34 * t35 - t41 * t42;
<a name="l00146"></a>00146     <span class="keyword">const</span> <span class="keywordtype">double</span> t45 = v1x0 * v1x0;
<a name="l00147"></a>00147     <span class="keyword">const</span> <span class="keywordtype">double</span> t46 = v1x1 * v1x1;
<a name="l00148"></a>00148     <span class="keyword">const</span> <span class="keywordtype">double</span> t47 = v1x2 * v1x2;
<a name="l00149"></a>00149     <span class="keyword">const</span> <span class="keywordtype">double</span> t49 = sqrt(t45 + t46 + t47);
<a name="l00150"></a>00150     <span class="keyword">const</span> <span class="keywordtype">double</span> t50 = t49 + Epsi;
<a name="l00151"></a>00151     <span class="keyword">const</span> <span class="keywordtype">double</span> t51 = sin(t50);
<a name="l00152"></a>00152     <span class="keyword">const</span> <span class="keywordtype">double</span> t52 = 0.1e1 / t49;
<a name="l00153"></a>00153     <span class="keyword">const</span> <span class="keywordtype">double</span> t53 = t51 * t52;
<a name="l00154"></a>00154     <span class="keyword">const</span> <span class="keywordtype">double</span> t54 = t53 * v1x0;
<a name="l00155"></a>00155     <span class="keyword">const</span> <span class="keywordtype">double</span> t55 = t45 * v1x0;
<a name="l00156"></a>00156     <span class="keyword">const</span> <span class="keywordtype">double</span> t56 = t50 * t50;
<a name="l00157"></a>00157     <span class="keyword">const</span> <span class="keywordtype">double</span> t57 = 0.1e1 / t56;
<a name="l00158"></a>00158     <span class="keyword">const</span> <span class="keywordtype">double</span> t60 = cos(t50);
<a name="l00159"></a>00159     <span class="keyword">const</span> <span class="keywordtype">double</span> t61 = 0.1e1 - t60;
<a name="l00160"></a>00160     <span class="keyword">const</span> <span class="keywordtype">double</span> t64 = t61 / t56 / t50;
<a name="l00161"></a>00161     <span class="keyword">const</span> <span class="keywordtype">double</span> t68 = t61 * t57;
<a name="l00162"></a>00162     <span class="keyword">const</span> <span class="keywordtype">double</span> t69 = t68 * v1x0;
<a name="l00163"></a>00163     <span class="keyword">const</span> <span class="keywordtype">double</span> t71 = -t54 + t53 * t55 * t57 - 0.2e1 * t64 * t55 * t52 + 0.2e1 * t69;
<a name="l00164"></a>00164     <span class="keyword">const</span> <span class="keywordtype">double</span> t74 = t11 + t15 * t1;
<a name="l00165"></a>00165     <span class="keyword">const</span> <span class="keywordtype">double</span> t75 = t74 * t33;
<a name="l00166"></a>00166     <span class="keyword">const</span> <span class="keywordtype">double</span> t77 = v2x3 - v1x3;
<a name="l00167"></a>00167     <span class="keyword">const</span> <span class="keywordtype">double</span> t79 = -t75 * t35 + t41 * t77;
<a name="l00168"></a>00168     <span class="keyword">const</span> <span class="keywordtype">double</span> t80 = t60 * t52;
<a name="l00169"></a>00169     <span class="keyword">const</span> <span class="keywordtype">double</span> t81 = 0.1e1 / t50;
<a name="l00170"></a>00170     <span class="keyword">const</span> <span class="keywordtype">double</span> t82 = v1x0 * t81;
<a name="l00171"></a>00171     <span class="keyword">const</span> <span class="keywordtype">double</span> t84 = t80 * t82 * v1x2;
<a name="l00172"></a>00172     <span class="keyword">const</span> <span class="keywordtype">double</span> t85 = t51 * t57;
<a name="l00173"></a>00173     <span class="keyword">const</span> <span class="keywordtype">double</span> t86 = v1x2 * t52;
<a name="l00174"></a>00174     <span class="keyword">const</span> <span class="keywordtype">double</span> t88 = t85 * t86 * v1x0;
<a name="l00175"></a>00175     <span class="keyword">const</span> <span class="keywordtype">double</span> t89 = t45 * t57;
<a name="l00176"></a>00176     <span class="keyword">const</span> <span class="keywordtype">double</span> t91 = t53 * t89 * v1x1;
<a name="l00177"></a>00177     <span class="keyword">const</span> <span class="keywordtype">double</span> t95 = 0.2e1 * t64 * t45 * v1x1 * t52;
<a name="l00178"></a>00178     <span class="keyword">const</span> <span class="keywordtype">double</span> t96 = t68 * v1x1;
<a name="l00179"></a>00179     <span class="keyword">const</span> <span class="keywordtype">double</span> t97 = -t84 + t88 + t91 - t95 + t96;
<a name="l00180"></a>00180     <span class="keyword">const</span> <span class="keywordtype">double</span> t101 = t75 * t42 - t34 * t77;
<a name="l00181"></a>00181     <span class="keyword">const</span> <span class="keywordtype">double</span> t103 = t80 * t82 * v1x1;
<a name="l00182"></a>00182     <span class="keyword">const</span> <span class="keywordtype">double</span> t106 = t85 * v1x1 * t52 * v1x0;
<a name="l00183"></a>00183     <span class="keyword">const</span> <span class="keywordtype">double</span> t108 = t53 * t89 * v1x2;
<a name="l00184"></a>00184     <span class="keyword">const</span> <span class="keywordtype">double</span> t112 = 0.2e1 * t64 * t45 * v1x2 * t52;
<a name="l00185"></a>00185     <span class="keyword">const</span> <span class="keywordtype">double</span> t113 = t68 * v1x2;
<a name="l00186"></a>00186     <span class="keyword">const</span> <span class="keywordtype">double</span> t114 = t103 - t106 + t108 - t112 + t113;
<a name="l00187"></a>00187     <span class="keyword">const</span> <span class="keywordtype">double</span> t117 = t53 * v1x1;
<a name="l00188"></a>00188     <span class="keyword">const</span> <span class="keywordtype">double</span> t118 = -t117 + t91 - t95;
<a name="l00189"></a>00189     <span class="keyword">const</span> <span class="keywordtype">double</span> t122 = t80 * v1x1 * t81 * v1x2;
<a name="l00190"></a>00190     <span class="keyword">const</span> <span class="keywordtype">double</span> t123 = t86 * v1x1;
<a name="l00191"></a>00191     <span class="keyword">const</span> <span class="keywordtype">double</span> t124 = t85 * t123;
<a name="l00192"></a>00192     <span class="keyword">const</span> <span class="keywordtype">double</span> t125 = t46 * t57;
<a name="l00193"></a>00193     <span class="keyword">const</span> <span class="keywordtype">double</span> t127 = t53 * t125 * v1x0;
<a name="l00194"></a>00194     <span class="keyword">const</span> <span class="keywordtype">double</span> t131 = 0.2e1 * t64 * v1x0 * t46 * t52;
<a name="l00195"></a>00195     <span class="keyword">const</span> <span class="keywordtype">double</span> t132 = -t122 + t124 + t127 - t131 + t69;
<a name="l00196"></a>00196     <span class="keyword">const</span> <span class="keywordtype">double</span> t135 = t80 * t46 * t81;
<a name="l00197"></a>00197     <span class="keyword">const</span> <span class="keywordtype">double</span> t137 = t85 * t46 * t52;
<a name="l00198"></a>00198     <span class="keyword">const</span> <span class="keywordtype">double</span> t138 = t51 * t81;
<a name="l00199"></a>00199     <span class="keyword">const</span> <span class="keywordtype">double</span> t141 = t117 * t57 * v1x0 * v1x2;
<a name="l00200"></a>00200     <span class="keyword">const</span> <span class="keywordtype">double</span> t144 = 0.2e1 * t64 * v1x0 * t123;
<a name="l00201"></a>00201     <span class="keyword">const</span> <span class="keywordtype">double</span> t145 = t135 - t137 + t138 + t141 - t144;
<a name="l00202"></a>00202     <span class="keyword">const</span> <span class="keywordtype">double</span> t148 = t53 * v1x2;
<a name="l00203"></a>00203     <span class="keyword">const</span> <span class="keywordtype">double</span> t149 = -t148 + t108 - t112;
<a name="l00204"></a>00204     <span class="keyword">const</span> <span class="keywordtype">double</span> t152 = t80 * t47 * t81;
<a name="l00205"></a>00205     <span class="keyword">const</span> <span class="keywordtype">double</span> t154 = t85 * t47 * t52;
<a name="l00206"></a>00206     <span class="keyword">const</span> <span class="keywordtype">double</span> t155 = -t152 + t154 - t138 + t141 - t144;
<a name="l00207"></a>00207     <span class="keyword">const</span> <span class="keywordtype">double</span> t157 = t47 * t57;
<a name="l00208"></a>00208     <span class="keyword">const</span> <span class="keywordtype">double</span> t159 = t53 * t157 * v1x0;
<a name="l00209"></a>00209     <span class="keyword">const</span> <span class="keywordtype">double</span> t163 = 0.2e1 * t64 * v1x0 * t47 * t52;
<a name="l00210"></a>00210     <span class="keyword">const</span> <span class="keywordtype">double</span> t164 = t122 - t124 + t159 - t163 + t69;
<a name="l00211"></a>00211     <span class="keyword">const</span> <span class="keywordtype">double</span> t168 = 0.1e1 / t32 / t31;
<a name="l00212"></a>00212     <span class="keyword">const</span> <span class="keywordtype">double</span> t169 = t18 * t168;
<a name="l00213"></a>00213     <span class="keyword">const</span> <span class="keywordtype">double</span> t170 = -2 * t35 * t77;
<a name="l00214"></a>00214     <span class="keyword">const</span> <span class="keywordtype">double</span> t171 = t169 * t170;
<a name="l00215"></a>00215     <span class="keyword">const</span> <span class="keywordtype">double</span> t172 = t40 * t168;
<a name="l00216"></a>00216     <span class="keyword">const</span> <span class="keywordtype">double</span> t173 = -2 * t42 * t77;
<a name="l00217"></a>00217     <span class="keyword">const</span> <span class="keywordtype">double</span> t174 = t172 * t173;
<a name="l00218"></a>00218     <span class="keyword">const</span> <span class="keywordtype">double</span> t175 = -t171 + t174;
<a name="l00219"></a>00219     <span class="keyword">const</span> <span class="keywordtype">double</span> t177 = t60 + t68 * t45;
<a name="l00220"></a>00220     <span class="keyword">const</span> <span class="keywordtype">double</span> t179 = t74 * t168;
<a name="l00221"></a>00221     <span class="keyword">const</span> <span class="keywordtype">double</span> t182 = -2 * t77 * t77;
<a name="l00222"></a>00222     <span class="keyword">const</span> <span class="keywordtype">double</span> t185 = t179 * t170 / 0.2e1 - t172 * t182 / 0.2e1 - t41;
<a name="l00223"></a>00223     <span class="keyword">const</span> <span class="keywordtype">double</span> t186 = t138 * v1x2;
<a name="l00224"></a>00224     <span class="keyword">const</span> <span class="keywordtype">double</span> t188 = t68 * v1x0 * v1x1;
<a name="l00225"></a>00225     <span class="keyword">const</span> <span class="keywordtype">double</span> t189 = -t186 + t188;
<a name="l00226"></a>00226     <span class="keyword">const</span> <span class="keywordtype">double</span> t195 = -t179 * t173 / 0.2e1 + t169 * t182 / 0.2e1 + t34;
<a name="l00227"></a>00227     <span class="keyword">const</span> <span class="keywordtype">double</span> t196 = t138 * v1x1;
<a name="l00228"></a>00228     <span class="keyword">const</span> <span class="keywordtype">double</span> t198 = t68 * v1x0 * v1x2;
<a name="l00229"></a>00229     <span class="keyword">const</span> <span class="keywordtype">double</span> t199 = t196 + t198;
<a name="l00230"></a>00230     <span class="keyword">const</span> <span class="keywordtype">double</span> t202 = -2 * t35 * t42;
<a name="l00231"></a>00231     <span class="keyword">const</span> <span class="keywordtype">double</span> t205 = -2 * t42 * t42;
<a name="l00232"></a>00232     <span class="keyword">const</span> <span class="keywordtype">double</span> t208 = -t169 * t202 / 0.2e1 + t172 * t205 / 0.2e1 + t41;
<a name="l00233"></a>00233     <span class="keyword">const</span> <span class="keywordtype">double</span> t210 = t179 * t202;
<a name="l00234"></a>00234     <span class="keyword">const</span> <span class="keywordtype">double</span> t211 = t210 - t174;
<a name="l00235"></a>00235     <span class="keyword">const</span> <span class="keywordtype">double</span> t217 = -t179 * t205 / 0.2e1 - t75 + t169 * t173 / 0.2e1;
<a name="l00236"></a>00236     <span class="keyword">const</span> <span class="keywordtype">double</span> t220 = -2 * t35 * t35;
<a name="l00237"></a>00237     <span class="keyword">const</span> <span class="keywordtype">double</span> t225 = -t169 * t220 / 0.2e1 - t34 + t172 * t202 / 0.2e1;
<a name="l00238"></a>00238     <span class="keyword">const</span> <span class="keywordtype">double</span> t231 = t179 * t220 / 0.2e1 + t75 - t172 * t170 / 0.2e1;
<a name="l00239"></a>00239     <span class="keyword">const</span> <span class="keywordtype">double</span> t233 = -t210 + t171;
<a name="l00240"></a>00240     <span class="keyword">const</span> <span class="keywordtype">double</span> t236 = 0.1e1 / t5;
<a name="l00241"></a>00241     <span class="keyword">const</span> <span class="keywordtype">double</span> t237 = t11 * t236;
<a name="l00242"></a>00242     <span class="keyword">const</span> <span class="keywordtype">double</span> t238 = v2x0 * t8;
<a name="l00243"></a>00243     <span class="keyword">const</span> <span class="keywordtype">double</span> t240 = t237 * t238 * v2x2;
<a name="l00244"></a>00244     <span class="keyword">const</span> <span class="keywordtype">double</span> t241 = t7 * t14;
<a name="l00245"></a>00245     <span class="keyword">const</span> <span class="keywordtype">double</span> t242 = v2x2 * t236;
<a name="l00246"></a>00246     <span class="keyword">const</span> <span class="keywordtype">double</span> t244 = t241 * t242 * v2x0;
<a name="l00247"></a>00247     <span class="keyword">const</span> <span class="keywordtype">double</span> t245 = t7 * t236;
<a name="l00248"></a>00248     <span class="keyword">const</span> <span class="keywordtype">double</span> t246 = t1 * t14;
<a name="l00249"></a>00249     <span class="keyword">const</span> <span class="keywordtype">double</span> t248 = t245 * t246 * v2x1;
<a name="l00250"></a>00250     <span class="keyword">const</span> <span class="keywordtype">double</span> t251 = t12 / t13 / t6;
<a name="l00251"></a>00251     <span class="keyword">const</span> <span class="keywordtype">double</span> t255 = 0.2e1 * t251 * t1 * v2x1 * t236;
<a name="l00252"></a>00252     <span class="keyword">const</span> <span class="keywordtype">double</span> t256 = t15 * v2x1;
<a name="l00253"></a>00253     <span class="keyword">const</span> <span class="keywordtype">double</span> t258 = (-t240 + t244 + t248 - t255 + t256) * t33;
<a name="l00254"></a>00254     <span class="keyword">const</span> <span class="keywordtype">double</span> t261 = t237 * t238 * v2x1;
<a name="l00255"></a>00255     <span class="keyword">const</span> <span class="keywordtype">double</span> t264 = t241 * v2x1 * t236 * v2x0;
<a name="l00256"></a>00256     <span class="keyword">const</span> <span class="keywordtype">double</span> t266 = t245 * t246 * v2x2;
<a name="l00257"></a>00257     <span class="keyword">const</span> <span class="keywordtype">double</span> t270 = 0.2e1 * t251 * t1 * v2x2 * t236;
<a name="l00258"></a>00258     <span class="keyword">const</span> <span class="keywordtype">double</span> t271 = t15 * v2x2;
<a name="l00259"></a>00259     <span class="keyword">const</span> <span class="keywordtype">double</span> t273 = (t261 - t264 + t266 - t270 + t271) * t33;
<a name="l00260"></a>00260     <span class="keyword">const</span> <span class="keywordtype">double</span> t275 = t258 * t35 - t273 * t42;
<a name="l00261"></a>00261     <span class="keyword">const</span> <span class="keywordtype">double</span> t277 = t245 * v2x0;
<a name="l00262"></a>00262     <span class="keyword">const</span> <span class="keywordtype">double</span> t278 = t1 * v2x0;
<a name="l00263"></a>00263     <span class="keyword">const</span> <span class="keywordtype">double</span> t284 = t15 * v2x0;
<a name="l00264"></a>00264     <span class="keyword">const</span> <span class="keywordtype">double</span> t287 = (-t277 + t245 * t278 * t14 - 0.2e1 * t251 * t278 * t236 + 0.2e1 * t284) * t33;
<a name="l00265"></a>00265     <span class="keyword">const</span> <span class="keywordtype">double</span> t290 = -t287 * t35 + t273 * t77;
<a name="l00266"></a>00266     <span class="keyword">const</span> <span class="keywordtype">double</span> t294 = t287 * t42 - t258 * t77;
<a name="l00267"></a>00267     <span class="keyword">const</span> <span class="keywordtype">double</span> t299 = t237 * v2x1 * t8 * v2x2;
<a name="l00268"></a>00268     <span class="keyword">const</span> <span class="keywordtype">double</span> t300 = t242 * v2x1;
<a name="l00269"></a>00269     <span class="keyword">const</span> <span class="keywordtype">double</span> t301 = t241 * t300;
<a name="l00270"></a>00270     <span class="keyword">const</span> <span class="keywordtype">double</span> t302 = t2 * t14;
<a name="l00271"></a>00271     <span class="keyword">const</span> <span class="keywordtype">double</span> t304 = t245 * t302 * v2x0;
<a name="l00272"></a>00272     <span class="keyword">const</span> <span class="keywordtype">double</span> t308 = 0.2e1 * t251 * v2x0 * t2 * t236;
<a name="l00273"></a>00273     <span class="keyword">const</span> <span class="keywordtype">double</span> t310 = (-t299 + t301 + t304 - t308 + t284) * t33;
<a name="l00274"></a>00274     <span class="keyword">const</span> <span class="keywordtype">double</span> t313 = t237 * t2 * t8;
<a name="l00275"></a>00275     <span class="keyword">const</span> <span class="keywordtype">double</span> t315 = t241 * t2 * t236;
<a name="l00276"></a>00276     <span class="keyword">const</span> <span class="keywordtype">double</span> t316 = t245 * v2x1;
<a name="l00277"></a>00277     <span class="keyword">const</span> <span class="keywordtype">double</span> t319 = t316 * t14 * v2x0 * v2x2;
<a name="l00278"></a>00278     <span class="keyword">const</span> <span class="keywordtype">double</span> t322 = 0.2e1 * t251 * v2x0 * t300;
<a name="l00279"></a>00279     <span class="keyword">const</span> <span class="keywordtype">double</span> t324 = (t313 - t315 + t9 + t319 - t322) * t33;
<a name="l00280"></a>00280     <span class="keyword">const</span> <span class="keywordtype">double</span> t326 = t310 * t35 - t324 * t42;
<a name="l00281"></a>00281     <span class="keyword">const</span> <span class="keywordtype">double</span> t329 = (-t316 + t248 - t255) * t33;
<a name="l00282"></a>00282     <span class="keyword">const</span> <span class="keywordtype">double</span> t332 = -t329 * t35 + t324 * t77;
<a name="l00283"></a>00283     <span class="keyword">const</span> <span class="keywordtype">double</span> t336 = t329 * t42 - t310 * t77;
<a name="l00284"></a>00284     <span class="keyword">const</span> <span class="keywordtype">double</span> t340 = t237 * t3 * t8;
<a name="l00285"></a>00285     <span class="keyword">const</span> <span class="keywordtype">double</span> t342 = t241 * t3 * t236;
<a name="l00286"></a>00286     <span class="keyword">const</span> <span class="keywordtype">double</span> t344 = (-t340 + t342 - t9 + t319 - t322) * t33;
<a name="l00287"></a>00287     <span class="keyword">const</span> <span class="keywordtype">double</span> t346 = t3 * t14;
<a name="l00288"></a>00288     <span class="keyword">const</span> <span class="keywordtype">double</span> t348 = t245 * t346 * v2x0;
<a name="l00289"></a>00289     <span class="keyword">const</span> <span class="keywordtype">double</span> t352 = 0.2e1 * t251 * v2x0 * t3 * t236;
<a name="l00290"></a>00290     <span class="keyword">const</span> <span class="keywordtype">double</span> t354 = (t299 - t301 + t348 - t352 + t284) * t33;
<a name="l00291"></a>00291     <span class="keyword">const</span> <span class="keywordtype">double</span> t356 = t344 * t35 - t354 * t42;
<a name="l00292"></a>00292     <span class="keyword">const</span> <span class="keywordtype">double</span> t358 = t245 * v2x2;
<a name="l00293"></a>00293     <span class="keyword">const</span> <span class="keywordtype">double</span> t360 = (-t358 + t266 - t270) * t33;
<a name="l00294"></a>00294     <span class="keyword">const</span> <span class="keywordtype">double</span> t363 = -t360 * t35 + t354 * t77;
<a name="l00295"></a>00295     <span class="keyword">const</span> <span class="keywordtype">double</span> t367 = t360 * t42 - t344 * t77;
<a name="l00296"></a>00296     <span class="keyword">const</span> <span class="keywordtype">double</span> t370 = 2 * t35 * t77;
<a name="l00297"></a>00297     <span class="keyword">const</span> <span class="keywordtype">double</span> t371 = t169 * t370;
<a name="l00298"></a>00298     <span class="keyword">const</span> <span class="keywordtype">double</span> t372 = 2 * t42 * t77;
<a name="l00299"></a>00299     <span class="keyword">const</span> <span class="keywordtype">double</span> t373 = t172 * t372;
<a name="l00300"></a>00300     <span class="keyword">const</span> <span class="keywordtype">double</span> t374 = -t371 + t373;
<a name="l00301"></a>00301     <span class="keyword">const</span> <span class="keywordtype">double</span> t378 = 2 * t77 * t77;
<a name="l00302"></a>00302     <span class="keyword">const</span> <span class="keywordtype">double</span> t381 = t179 * t370 / 0.2e1 - t172 * t378 / 0.2e1 + t41;
<a name="l00303"></a>00303     <span class="keyword">const</span> <span class="keywordtype">double</span> t387 = -t179 * t372 / 0.2e1 + t169 * t378 / 0.2e1 - t34;
<a name="l00304"></a>00304     <span class="keyword">const</span> <span class="keywordtype">double</span> t390 = 2 * t35 * t42;
<a name="l00305"></a>00305     <span class="keyword">const</span> <span class="keywordtype">double</span> t393 = 2 * t42 * t42;
<a name="l00306"></a>00306     <span class="keyword">const</span> <span class="keywordtype">double</span> t396 = -t169 * t390 / 0.2e1 + t172 * t393 / 0.2e1 - t41;
<a name="l00307"></a>00307     <span class="keyword">const</span> <span class="keywordtype">double</span> t398 = t179 * t390;
<a name="l00308"></a>00308     <span class="keyword">const</span> <span class="keywordtype">double</span> t399 = t398 - t373;
<a name="l00309"></a>00309     <span class="keyword">const</span> <span class="keywordtype">double</span> t405 = -t179 * t393 / 0.2e1 + t75 + t169 * t372 / 0.2e1;
<a name="l00310"></a>00310     <span class="keyword">const</span> <span class="keywordtype">double</span> t408 = 2 * t35 * t35;
<a name="l00311"></a>00311     <span class="keyword">const</span> <span class="keywordtype">double</span> t413 = -t169 * t408 / 0.2e1 + t34 + t172 * t390 / 0.2e1;
<a name="l00312"></a>00312     <span class="keyword">const</span> <span class="keywordtype">double</span> t419 = t179 * t408 / 0.2e1 - t75 - t172 * t370 / 0.2e1;
<a name="l00313"></a>00313     <span class="keyword">const</span> <span class="keywordtype">double</span> t421 = -t398 + t371;
<a name="l00314"></a>00314     <span class="keyword">const</span> <span class="keywordtype">double</span> t428 = t84 - t88 + t91 - t95 + t96;
<a name="l00315"></a>00315     <span class="keyword">const</span> <span class="keywordtype">double</span> t430 = -t54 + t127 - t131;
<a name="l00316"></a>00316     <span class="keyword">const</span> <span class="keywordtype">double</span> t433 = t80 * t45 * t81;
<a name="l00317"></a>00317     <span class="keyword">const</span> <span class="keywordtype">double</span> t435 = t85 * t45 * t52;
<a name="l00318"></a>00318     <span class="keyword">const</span> <span class="keywordtype">double</span> t436 = -t433 + t435 - t138 + t141 - t144;
<a name="l00319"></a>00319     <span class="keyword">const</span> <span class="keywordtype">double</span> t439 = t122 - t124 + t127 - t131 + t69;
<a name="l00320"></a>00320     <span class="keyword">const</span> <span class="keywordtype">double</span> t441 = t46 * v1x1;
<a name="l00321"></a>00321     <span class="keyword">const</span> <span class="keywordtype">double</span> t448 = -t117 + t53 * t441 * t57 - 0.2e1 * t64 * t441 * t52 + 0.2e1 * t96;
<a name="l00322"></a>00322     <span class="keyword">const</span> <span class="keywordtype">double</span> t451 = t53 * t125 * v1x2;
<a name="l00323"></a>00323     <span class="keyword">const</span> <span class="keywordtype">double</span> t455 = 0.2e1 * t64 * t46 * v1x2 * t52;
<a name="l00324"></a>00324     <span class="keyword">const</span> <span class="keywordtype">double</span> t456 = -t103 + t106 + t451 - t455 + t113;
<a name="l00325"></a>00325     <span class="keyword">const</span> <span class="keywordtype">double</span> t459 = t152 - t154 + t138 + t141 - t144;
<a name="l00326"></a>00326     <span class="keyword">const</span> <span class="keywordtype">double</span> t461 = -t148 + t451 - t455;
<a name="l00327"></a>00327     <span class="keyword">const</span> <span class="keywordtype">double</span> t464 = t53 * t157 * v1x1;
<a name="l00328"></a>00328     <span class="keyword">const</span> <span class="keywordtype">double</span> t468 = 0.2e1 * t64 * v1x1 * t47 * t52;
<a name="l00329"></a>00329     <span class="keyword">const</span> <span class="keywordtype">double</span> t469 = -t84 + t88 + t464 - t468 + t96;
<a name="l00330"></a>00330     <span class="keyword">const</span> <span class="keywordtype">double</span> t472 = t186 + t188;
<a name="l00331"></a>00331     <span class="keyword">const</span> <span class="keywordtype">double</span> t475 = t60 + t68 * t46;
<a name="l00332"></a>00332     <span class="keyword">const</span> <span class="keywordtype">double</span> t477 = t138 * v1x0;
<a name="l00333"></a>00333     <span class="keyword">const</span> <span class="keywordtype">double</span> t479 = t68 * v1x1 * v1x2;
<a name="l00334"></a>00334     <span class="keyword">const</span> <span class="keywordtype">double</span> t480 = -t477 + t479;
<a name="l00335"></a>00335     <span class="keyword">const</span> <span class="keywordtype">double</span> t519 = -t103 + t106 + t108 - t112 + t113;
<a name="l00336"></a>00336     <span class="keyword">const</span> <span class="keywordtype">double</span> t521 = t433 - t435 + t138 + t141 - t144;
<a name="l00337"></a>00337     <span class="keyword">const</span> <span class="keywordtype">double</span> t523 = -t54 + t159 - t163;
<a name="l00338"></a>00338     <span class="keyword">const</span> <span class="keywordtype">double</span> t526 = -t135 + t137 - t138 + t141 - t144;
<a name="l00339"></a>00339     <span class="keyword">const</span> <span class="keywordtype">double</span> t528 = t103 - t106 + t451 - t455 + t113;
<a name="l00340"></a>00340     <span class="keyword">const</span> <span class="keywordtype">double</span> t530 = -t117 + t464 - t468;
<a name="l00341"></a>00341     <span class="keyword">const</span> <span class="keywordtype">double</span> t533 = -t122 + t124 + t159 - t163 + t69;
<a name="l00342"></a>00342     <span class="keyword">const</span> <span class="keywordtype">double</span> t535 = t84 - t88 + t464 - t468 + t96;
<a name="l00343"></a>00343     <span class="keyword">const</span> <span class="keywordtype">double</span> t537 = t47 * v1x2;
<a name="l00344"></a>00344     <span class="keyword">const</span> <span class="keywordtype">double</span> t544 = -t148 + t53 * t537 * t57 - 0.2e1 * t64 * t537 * t52 + 0.2e1 * t113;
<a name="l00345"></a>00345     <span class="keyword">const</span> <span class="keywordtype">double</span> t547 = -t196 + t198;
<a name="l00346"></a>00346     <span class="keyword">const</span> <span class="keywordtype">double</span> t549 = t477 + t479;
<a name="l00347"></a>00347     <span class="keyword">const</span> <span class="keywordtype">double</span> t552 = t60 + t68 * t47;
<a name="l00348"></a>00348     <span class="keyword">const</span> <span class="keywordtype">double</span> t592 = t11 + t15 * t2;
<a name="l00349"></a>00349     <span class="keyword">const</span> <span class="keywordtype">double</span> t593 = t592 * t33;
<a name="l00350"></a>00350     <span class="keyword">const</span> <span class="keywordtype">double</span> t595 = t9 * v2x0;
<a name="l00351"></a>00351     <span class="keyword">const</span> <span class="keywordtype">double</span> t597 = t15 * v2x1 * v2x2;
<a name="l00352"></a>00352     <span class="keyword">const</span> <span class="keywordtype">double</span> t598 = -t595 + t597;
<a name="l00353"></a>00353     <span class="keyword">const</span> <span class="keywordtype">double</span> t599 = t598 * t33;
<a name="l00354"></a>00354     <span class="keyword">const</span> <span class="keywordtype">double</span> t601 = t593 * t35 - t599 * t42;
<a name="l00355"></a>00355     <span class="keyword">const</span> <span class="keywordtype">double</span> t603 = t10 + t17;
<a name="l00356"></a>00356     <span class="keyword">const</span> <span class="keywordtype">double</span> t604 = t603 * t33;
<a name="l00357"></a>00357     <span class="keyword">const</span> <span class="keywordtype">double</span> t607 = -t604 * t35 + t599 * t77;
<a name="l00358"></a>00358     <span class="keyword">const</span> <span class="keywordtype">double</span> t611 = t604 * t42 - t593 * t77;
<a name="l00359"></a>00359     <span class="keyword">const</span> <span class="keywordtype">double</span> t622 = t592 * t168;
<a name="l00360"></a>00360     <span class="keyword">const</span> <span class="keywordtype">double</span> t623 = t622 * t170;
<a name="l00361"></a>00361     <span class="keyword">const</span> <span class="keywordtype">double</span> t624 = t598 * t168;
<a name="l00362"></a>00362     <span class="keyword">const</span> <span class="keywordtype">double</span> t625 = t624 * t173;
<a name="l00363"></a>00363     <span class="keyword">const</span> <span class="keywordtype">double</span> t626 = -t623 + t625;
<a name="l00364"></a>00364     <span class="keyword">const</span> <span class="keywordtype">double</span> t628 = t603 * t168;
<a name="l00365"></a>00365     <span class="keyword">const</span> <span class="keywordtype">double</span> t633 = t628 * t170 / 0.2e1 - t624 * t182 / 0.2e1 - t599;
<a name="l00366"></a>00366     <span class="keyword">const</span> <span class="keywordtype">double</span> t639 = -t628 * t173 / 0.2e1 + t622 * t182 / 0.2e1 + t593;
<a name="l00367"></a>00367     <span class="keyword">const</span> <span class="keywordtype">double</span> t646 = -t622 * t202 / 0.2e1 + t624 * t205 / 0.2e1 + t599;
<a name="l00368"></a>00368     <span class="keyword">const</span> <span class="keywordtype">double</span> t648 = t628 * t202;
<a name="l00369"></a>00369     <span class="keyword">const</span> <span class="keywordtype">double</span> t649 = t648 - t625;
<a name="l00370"></a>00370     <span class="keyword">const</span> <span class="keywordtype">double</span> t655 = -t628 * t205 / 0.2e1 - t604 + t622 * t173 / 0.2e1;
<a name="l00371"></a>00371     <span class="keyword">const</span> <span class="keywordtype">double</span> t662 = -t622 * t220 / 0.2e1 - t593 + t624 * t202 / 0.2e1;
<a name="l00372"></a>00372     <span class="keyword">const</span> <span class="keywordtype">double</span> t668 = t628 * t220 / 0.2e1 + t604 - t624 * t170 / 0.2e1;
<a name="l00373"></a>00373     <span class="keyword">const</span> <span class="keywordtype">double</span> t670 = -t648 + t623;
<a name="l00374"></a>00374     <span class="keyword">const</span> <span class="keywordtype">double</span> t674 = (-t277 + t304 - t308) * t33;
<a name="l00375"></a>00375     <span class="keyword">const</span> <span class="keywordtype">double</span> t677 = t237 * t1 * t8;
<a name="l00376"></a>00376     <span class="keyword">const</span> <span class="keywordtype">double</span> t679 = t241 * t1 * t236;
<a name="l00377"></a>00377     <span class="keyword">const</span> <span class="keywordtype">double</span> t681 = (-t677 + t679 - t9 + t319 - t322) * t33;
<a name="l00378"></a>00378     <span class="keyword">const</span> <span class="keywordtype">double</span> t683 = t674 * t35 - t681 * t42;
<a name="l00379"></a>00379     <span class="keyword">const</span> <span class="keywordtype">double</span> t686 = (t240 - t244 + t248 - t255 + t256) * t33;
<a name="l00380"></a>00380     <span class="keyword">const</span> <span class="keywordtype">double</span> t689 = -t686 * t35 + t681 * t77;
<a name="l00381"></a>00381     <span class="keyword">const</span> <span class="keywordtype">double</span> t693 = t686 * t42 - t674 * t77;
<a name="l00382"></a>00382     <span class="keyword">const</span> <span class="keywordtype">double</span> t696 = t2 * v2x1;
<a name="l00383"></a>00383     <span class="keyword">const</span> <span class="keywordtype">double</span> t704 = (-t316 + t245 * t696 * t14 - 0.2e1 * t251 * t696 * t236 + 0.2e1 * t256) * t33;
<a name="l00384"></a>00384     <span class="keyword">const</span> <span class="keywordtype">double</span> t707 = t245 * t302 * v2x2;
<a name="l00385"></a>00385     <span class="keyword">const</span> <span class="keywordtype">double</span> t711 = 0.2e1 * t251 * t2 * v2x2 * t236;
<a name="l00386"></a>00386     <span class="keyword">const</span> <span class="keywordtype">double</span> t713 = (-t261 + t264 + t707 - t711 + t271) * t33;
<a name="l00387"></a>00387     <span class="keyword">const</span> <span class="keywordtype">double</span> t715 = t704 * t35 - t713 * t42;
<a name="l00388"></a>00388     <span class="keyword">const</span> <span class="keywordtype">double</span> t718 = (t299 - t301 + t304 - t308 + t284) * t33;
<a name="l00389"></a>00389     <span class="keyword">const</span> <span class="keywordtype">double</span> t721 = -t718 * t35 + t713 * t77;
<a name="l00390"></a>00390     <span class="keyword">const</span> <span class="keywordtype">double</span> t725 = t718 * t42 - t704 * t77;
<a name="l00391"></a>00391     <span class="keyword">const</span> <span class="keywordtype">double</span> t729 = (-t358 + t707 - t711) * t33;
<a name="l00392"></a>00392     <span class="keyword">const</span> <span class="keywordtype">double</span> t732 = t245 * t346 * v2x1;
<a name="l00393"></a>00393     <span class="keyword">const</span> <span class="keywordtype">double</span> t736 = 0.2e1 * t251 * v2x1 * t3 * t236;
<a name="l00394"></a>00394     <span class="keyword">const</span> <span class="keywordtype">double</span> t738 = (-t240 + t244 + t732 - t736 + t256) * t33;
<a name="l00395"></a>00395     <span class="keyword">const</span> <span class="keywordtype">double</span> t740 = t729 * t35 - t738 * t42;
<a name="l00396"></a>00396     <span class="keyword">const</span> <span class="keywordtype">double</span> t743 = (t340 - t342 + t9 + t319 - t322) * t33;
<a name="l00397"></a>00397     <span class="keyword">const</span> <span class="keywordtype">double</span> t746 = -t743 * t35 + t738 * t77;
<a name="l00398"></a>00398     <span class="keyword">const</span> <span class="keywordtype">double</span> t750 = t743 * t42 - t729 * t77;
<a name="l00399"></a>00399     <span class="keyword">const</span> <span class="keywordtype">double</span> t753 = t622 * t370;
<a name="l00400"></a>00400     <span class="keyword">const</span> <span class="keywordtype">double</span> t754 = t624 * t372;
<a name="l00401"></a>00401     <span class="keyword">const</span> <span class="keywordtype">double</span> t755 = -t753 + t754;
<a name="l00402"></a>00402     <span class="keyword">const</span> <span class="keywordtype">double</span> t761 = t628 * t370 / 0.2e1 - t624 * t378 / 0.2e1 + t599;
<a name="l00403"></a>00403     <span class="keyword">const</span> <span class="keywordtype">double</span> t767 = -t628 * t372 / 0.2e1 + t622 * t378 / 0.2e1 - t593;
<a name="l00404"></a>00404     <span class="keyword">const</span> <span class="keywordtype">double</span> t774 = -t622 * t390 / 0.2e1 + t624 * t393 / 0.2e1 - t599;
<a name="l00405"></a>00405     <span class="keyword">const</span> <span class="keywordtype">double</span> t776 = t628 * t390;
<a name="l00406"></a>00406     <span class="keyword">const</span> <span class="keywordtype">double</span> t777 = t776 - t754;
<a name="l00407"></a>00407     <span class="keyword">const</span> <span class="keywordtype">double</span> t783 = -t628 * t393 / 0.2e1 + t604 + t622 * t372 / 0.2e1;
<a name="l00408"></a>00408     <span class="keyword">const</span> <span class="keywordtype">double</span> t790 = -t622 * t408 / 0.2e1 + t593 + t624 * t390 / 0.2e1;
<a name="l00409"></a>00409     <span class="keyword">const</span> <span class="keywordtype">double</span> t796 = t628 * t408 / 0.2e1 - t604 - t624 * t370 / 0.2e1;
<a name="l00410"></a>00410     <span class="keyword">const</span> <span class="keywordtype">double</span> t798 = -t776 + t753;
<a name="l00411"></a>00411     <span class="keyword">const</span> <span class="keywordtype">double</span> t909 = t595 + t597;
<a name="l00412"></a>00412     <span class="keyword">const</span> <span class="keywordtype">double</span> t910 = t909 * t33;
<a name="l00413"></a>00413     <span class="keyword">const</span> <span class="keywordtype">double</span> t913 = t11 + t15 * t3;
<a name="l00414"></a>00414     <span class="keyword">const</span> <span class="keywordtype">double</span> t914 = t913 * t33;
<a name="l00415"></a>00415     <span class="keyword">const</span> <span class="keywordtype">double</span> t916 = t910 * t35 - t914 * t42;
<a name="l00416"></a>00416     <span class="keyword">const</span> <span class="keywordtype">double</span> t918 = -t37 + t39;
<a name="l00417"></a>00417     <span class="keyword">const</span> <span class="keywordtype">double</span> t919 = t918 * t33;
<a name="l00418"></a>00418     <span class="keyword">const</span> <span class="keywordtype">double</span> t922 = -t919 * t35 + t914 * t77;
<a name="l00419"></a>00419     <span class="keyword">const</span> <span class="keywordtype">double</span> t926 = t919 * t42 - t910 * t77;
<a name="l00420"></a>00420     <span class="keyword">const</span> <span class="keywordtype">double</span> t937 = t909 * t168;
<a name="l00421"></a>00421     <span class="keyword">const</span> <span class="keywordtype">double</span> t938 = t937 * t170;
<a name="l00422"></a>00422     <span class="keyword">const</span> <span class="keywordtype">double</span> t939 = t913 * t168;
<a name="l00423"></a>00423     <span class="keyword">const</span> <span class="keywordtype">double</span> t940 = t939 * t173;
<a name="l00424"></a>00424     <span class="keyword">const</span> <span class="keywordtype">double</span> t941 = -t938 + t940;
<a name="l00425"></a>00425     <span class="keyword">const</span> <span class="keywordtype">double</span> t943 = t918 * t168;
<a name="l00426"></a>00426     <span class="keyword">const</span> <span class="keywordtype">double</span> t948 = t943 * t170 / 0.2e1 - t939 * t182 / 0.2e1 - t914;
<a name="l00427"></a>00427     <span class="keyword">const</span> <span class="keywordtype">double</span> t954 = -t943 * t173 / 0.2e1 + t937 * t182 / 0.2e1 + t910;
<a name="l00428"></a>00428     <span class="keyword">const</span> <span class="keywordtype">double</span> t961 = -t937 * t202 / 0.2e1 + t939 * t205 / 0.2e1 + t914;
<a name="l00429"></a>00429     <span class="keyword">const</span> <span class="keywordtype">double</span> t963 = t943 * t202;
<a name="l00430"></a>00430     <span class="keyword">const</span> <span class="keywordtype">double</span> t964 = t963 - t940;
<a name="l00431"></a>00431     <span class="keyword">const</span> <span class="keywordtype">double</span> t970 = -t943 * t205 / 0.2e1 - t919 + t937 * t173 / 0.2e1;
<a name="l00432"></a>00432     <span class="keyword">const</span> <span class="keywordtype">double</span> t977 = -t937 * t220 / 0.2e1 - t910 + t939 * t202 / 0.2e1;
<a name="l00433"></a>00433     <span class="keyword">const</span> <span class="keywordtype">double</span> t983 = t943 * t220 / 0.2e1 + t919 - t939 * t170 / 0.2e1;
<a name="l00434"></a>00434     <span class="keyword">const</span> <span class="keywordtype">double</span> t985 = -t963 + t938;
<a name="l00435"></a>00435     <span class="keyword">const</span> <span class="keywordtype">double</span> t989 = (t677 - t679 + t9 + t319 - t322) * t33;
<a name="l00436"></a>00436     <span class="keyword">const</span> <span class="keywordtype">double</span> t992 = (-t277 + t348 - t352) * t33;
<a name="l00437"></a>00437     <span class="keyword">const</span> <span class="keywordtype">double</span> t994 = t989 * t35 - t992 * t42;
<a name="l00438"></a>00438     <span class="keyword">const</span> <span class="keywordtype">double</span> t997 = (-t261 + t264 + t266 - t270 + t271) * t33;
<a name="l00439"></a>00439     <span class="keyword">const</span> <span class="keywordtype">double</span> t1000 = -t997 * t35 + t992 * t77;
<a name="l00440"></a>00440     <span class="keyword">const</span> <span class="keywordtype">double</span> t1004 = t997 * t42 - t989 * t77;
<a name="l00441"></a>00441     <span class="keyword">const</span> <span class="keywordtype">double</span> t1008 = (t261 - t264 + t707 - t711 + t271) * t33;
<a name="l00442"></a>00442     <span class="keyword">const</span> <span class="keywordtype">double</span> t1011 = (-t316 + t732 - t736) * t33;
<a name="l00443"></a>00443     <span class="keyword">const</span> <span class="keywordtype">double</span> t1013 = t1008 * t35 - t1011 * t42;
<a name="l00444"></a>00444     <span class="keyword">const</span> <span class="keywordtype">double</span> t1016 = (-t313 + t315 - t9 + t319 - t322) * t33;
<a name="l00445"></a>00445     <span class="keyword">const</span> <span class="keywordtype">double</span> t1019 = -t1016 * t35 + t1011 * t77;
<a name="l00446"></a>00446     <span class="keyword">const</span> <span class="keywordtype">double</span> t1023 = t1016 * t42 - t1008 * t77;
<a name="l00447"></a>00447     <span class="keyword">const</span> <span class="keywordtype">double</span> t1027 = (t240 - t244 + t732 - t736 + t256) * t33;
<a name="l00448"></a>00448     <span class="keyword">const</span> <span class="keywordtype">double</span> t1029 = t3 * v2x2;
<a name="l00449"></a>00449     <span class="keyword">const</span> <span class="keywordtype">double</span> t1037 = (-t358 + t245 * t1029 * t14 - 0.2e1 * t251 * t1029 * t236 + 0.2e1 * t271) * t33;
<a name="l00450"></a>00450     <span class="keyword">const</span> <span class="keywordtype">double</span> t1039 = t1027 * t35 - t1037 * t42;
<a name="l00451"></a>00451     <span class="keyword">const</span> <span class="keywordtype">double</span> t1042 = (-t299 + t301 + t348 - t352 + t284) * t33;
<a name="l00452"></a>00452     <span class="keyword">const</span> <span class="keywordtype">double</span> t1045 = -t1042 * t35 + t1037 * t77;
<a name="l00453"></a>00453     <span class="keyword">const</span> <span class="keywordtype">double</span> t1049 = t1042 * t42 - t1027 * t77;
<a name="l00454"></a>00454     <span class="keyword">const</span> <span class="keywordtype">double</span> t1052 = t937 * t370;
<a name="l00455"></a>00455     <span class="keyword">const</span> <span class="keywordtype">double</span> t1053 = t939 * t372;
<a name="l00456"></a>00456     <span class="keyword">const</span> <span class="keywordtype">double</span> t1054 = -t1052 + t1053;
<a name="l00457"></a>00457     <span class="keyword">const</span> <span class="keywordtype">double</span> t1060 = t943 * t370 / 0.2e1 - t939 * t378 / 0.2e1 + t914;
<a name="l00458"></a>00458     <span class="keyword">const</span> <span class="keywordtype">double</span> t1066 = -t943 * t372 / 0.2e1 + t937 * t378 / 0.2e1 - t910;
<a name="l00459"></a>00459     <span class="keyword">const</span> <span class="keywordtype">double</span> t1073 = -t937 * t390 / 0.2e1 + t939 * t393 / 0.2e1 - t914;
<a name="l00460"></a>00460     <span class="keyword">const</span> <span class="keywordtype">double</span> t1075 = t943 * t390;
<a name="l00461"></a>00461     <span class="keyword">const</span> <span class="keywordtype">double</span> t1076 = t1075 - t1053;
<a name="l00462"></a>00462     <span class="keyword">const</span> <span class="keywordtype">double</span> t1082 = -t943 * t393 / 0.2e1 + t919 + t937 * t372 / 0.2e1;
<a name="l00463"></a>00463     <span class="keyword">const</span> <span class="keywordtype">double</span> t1089 = -t937 * t408 / 0.2e1 + t910 + t939 * t390 / 0.2e1;
<a name="l00464"></a>00464     <span class="keyword">const</span> <span class="keywordtype">double</span> t1095 = t943 * t408 / 0.2e1 - t919 - t939 * t370 / 0.2e1;
<a name="l00465"></a>00465     <span class="keyword">const</span> <span class="keywordtype">double</span> t1097 = -t1075 + t1052;
<a name="l00466"></a>00466 
<a name="l00467"></a>00467     cg0[13*0+0] = t44 * t71 + t79 * t97 + t101 * t114;
<a name="l00468"></a>00468     cg0[13*0+1] = t44 * t118 + t79 * t132 + t101 * t145;
<a name="l00469"></a>00469     cg0[13*0+2] = t44 * t149 + t79 * t155 + t101 * t164;
<a name="l00470"></a>00470     cg0[13*0+3] = t175 * t177 / 0.2e1 + t185 * t189 + t195 * t199;
<a name="l00471"></a>00471     cg0[13*0+4] = t208 * t177 + t211 * t189 / 0.2e1 + t217 * t199;
<a name="l00472"></a>00472     cg0[13*0+5] = t225 * t177 + t231 * t189 + t233 * t199 / 0.2e1;
<a name="l00473"></a>00473     cg0[13*0+6] = t275 * t177 + t290 * t189 + t294 * t199;
<a name="l00474"></a>00474     cg0[13*0+7] = t326 * t177 + t332 * t189 + t336 * t199;
<a name="l00475"></a>00475     cg0[13*0+8] = t356 * t177 + t363 * t189 + t367 * t199;
<a name="l00476"></a>00476     cg0[13*0+9] = t374 * t177 / 0.2e1 + t381 * t189 + t387 * t199;
<a name="l00477"></a>00477     cg0[13*0+10] = t396 * t177 + t399 * t189 / 0.2e1 + t405 * t199;
<a name="l00478"></a>00478     cg0[13*0+11] = t413 * t177 + t419 * t189 + t421 * t199 / 0.2e1;
<a name="l00479"></a>00479     cg0[13*0+12] = t44 * t177 + t79 * t189 + t101 * t199;
<a name="l00480"></a>00480     cg0[13*1+0] = t44 * t428 + t79 * t430 + t101 * t436;
<a name="l00481"></a>00481     cg0[13*1+1] = t44 * t439 + t79 * t448 + t101 * t456;
<a name="l00482"></a>00482     cg0[13*1+2] = t44 * t459 + t79 * t461 + t101 * t469;
<a name="l00483"></a>00483     cg0[13*1+3] = t175 * t472 / 0.2e1 + t185 * t475 + t195 * t480;
<a name="l00484"></a>00484     cg0[13*1+4] = t208 * t472 + t211 * t475 / 0.2e1 + t217 * t480;
<a name="l00485"></a>00485     cg0[13*1+5] = t225 * t472 + t231 * t475 + t233 * t480 / 0.2e1;
<a name="l00486"></a>00486     cg0[13*1+6] = t275 * t472 + t290 * t475 + t294 * t480;
<a name="l00487"></a>00487     cg0[13*1+7] = t326 * t472 + t332 * t475 + t336 * t480;
<a name="l00488"></a>00488     cg0[13*1+8] = t356 * t472 + t363 * t475 + t367 * t480;
<a name="l00489"></a>00489     cg0[13*1+9] = t374 * t472 / 0.2e1 + t381 * t475 + t387 * t480;
<a name="l00490"></a>00490     cg0[13*1+10] = t396 * t472 + t399 * t475 / 0.2e1 + t405 * t480;
<a name="l00491"></a>00491     cg0[13*1+11] = t413 * t472 + t419 * t475 + t421 * t480 / 0.2e1;
<a name="l00492"></a>00492     cg0[13*1+12] = t44 * t472 + t79 * t475 + t101 * t480;
<a name="l00493"></a>00493     cg0[13*2+0] = t44 * t519 + t79 * t521 + t101 * t523;
<a name="l00494"></a>00494     cg0[13*2+1] = t44 * t526 + t79 * t528 + t101 * t530;
<a name="l00495"></a>00495     cg0[13*2+2] = t44 * t533 + t79 * t535 + t101 * t544;
<a name="l00496"></a>00496     cg0[13*2+3] = t175 * t547 / 0.2e1 + t185 * t549 + t195 * t552;
<a name="l00497"></a>00497     cg0[13*2+4] = t208 * t547 + t211 * t549 / 0.2e1 + t217 * t552;
<a name="l00498"></a>00498     cg0[13*2+5] = t225 * t547 + t231 * t549 + t233 * t552 / 0.2e1;
<a name="l00499"></a>00499     cg0[13*2+6] = t275 * t547 + t290 * t549 + t294 * t552;
<a name="l00500"></a>00500     cg0[13*2+7] = t326 * t547 + t332 * t549 + t336 * t552;
<a name="l00501"></a>00501     cg0[13*2+8] = t356 * t547 + t363 * t549 + t367 * t552;
<a name="l00502"></a>00502     cg0[13*2+9] = t374 * t547 / 0.2e1 + t381 * t549 + t387 * t552;
<a name="l00503"></a>00503     cg0[13*2+10] = t396 * t547 + t399 * t549 / 0.2e1 + t405 * t552;
<a name="l00504"></a>00504     cg0[13*2+11] = t413 * t547 + t419 * t549 + t421 * t552 / 0.2e1;
<a name="l00505"></a>00505     cg0[13*2+12] = t44 * t547 + t79 * t549 + t101 * t552;
<a name="l00506"></a>00506     cg0[13*3+0] = t601 * t71 + t607 * t97 + t611 * t114;
<a name="l00507"></a>00507     cg0[13*3+1] = t601 * t118 + t607 * t132 + t611 * t145;
<a name="l00508"></a>00508     cg0[13*3+2] = t601 * t149 + t607 * t155 + t611 * t164;
<a name="l00509"></a>00509     cg0[13*3+3] = t626 * t177 / 0.2e1 + t633 * t189 + t639 * t199;
<a name="l00510"></a>00510     cg0[13*3+4] = t646 * t177 + t649 * t189 / 0.2e1 + t655 * t199;
<a name="l00511"></a>00511     cg0[13*3+5] = t662 * t177 + t668 * t189 + t670 * t199 / 0.2e1;
<a name="l00512"></a>00512     cg0[13*3+6] = t683 * t177 + t689 * t189 + t693 * t199;
<a name="l00513"></a>00513     cg0[13*3+7] = t715 * t177 + t721 * t189 + t725 * t199;
<a name="l00514"></a>00514     cg0[13*3+8] = t740 * t177 + t746 * t189 + t750 * t199;
<a name="l00515"></a>00515     cg0[13*3+9] = t755 * t177 / 0.2e1 + t761 * t189 + t767 * t199;
<a name="l00516"></a>00516     cg0[13*3+10] = t774 * t177 + t777 * t189 / 0.2e1 + t783 * t199;
<a name="l00517"></a>00517     cg0[13*3+11] = t790 * t177 + t796 * t189 + t798 * t199 / 0.2e1;
<a name="l00518"></a>00518     cg0[13*3+12] = t601 * t177 + t607 * t189 + t611 * t199;
<a name="l00519"></a>00519     cg0[13*4+0] = t601 * t428 + t607 * t430 + t611 * t436;
<a name="l00520"></a>00520     cg0[13*4+1] = t601 * t439 + t607 * t448 + t611 * t456;
<a name="l00521"></a>00521     cg0[13*4+2] = t601 * t459 + t607 * t461 + t611 * t469;
<a name="l00522"></a>00522     cg0[13*4+3] = t626 * t472 / 0.2e1 + t633 * t475 + t639 * t480;
<a name="l00523"></a>00523     cg0[13*4+4] = t646 * t472 + t649 * t475 / 0.2e1 + t655 * t480;
<a name="l00524"></a>00524     cg0[13*4+5] = t662 * t472 + t668 * t475 + t670 * t480 / 0.2e1;
<a name="l00525"></a>00525     cg0[13*4+6] = t683 * t472 + t689 * t475 + t693 * t480;
<a name="l00526"></a>00526     cg0[13*4+7] = t715 * t472 + t721 * t475 + t725 * t480;
<a name="l00527"></a>00527     cg0[13*4+8] = t740 * t472 + t746 * t475 + t750 * t480;
<a name="l00528"></a>00528     cg0[13*4+9] = t755 * t472 / 0.2e1 + t761 * t475 + t767 * t480;
<a name="l00529"></a>00529     cg0[13*4+10] = t774 * t472 + t777 * t475 / 0.2e1 + t783 * t480;
<a name="l00530"></a>00530     cg0[13*4+11] = t790 * t472 + t796 * t475 + t798 * t480 / 0.2e1;
<a name="l00531"></a>00531     cg0[13*4+12] = t601 * t472 + t607 * t475 + t611 * t480;
<a name="l00532"></a>00532     cg0[13*5+0] = t601 * t519 + t607 * t521 + t611 * t523;
<a name="l00533"></a>00533     cg0[13*5+1] = t601 * t526 + t607 * t528 + t611 * t530;
<a name="l00534"></a>00534     cg0[13*5+2] = t601 * t533 + t607 * t535 + t611 * t544;
<a name="l00535"></a>00535     cg0[13*5+3] = t626 * t547 / 0.2e1 + t633 * t549 + t639 * t552;
<a name="l00536"></a>00536     cg0[13*5+4] = t646 * t547 + t649 * t549 / 0.2e1 + t655 * t552;
<a name="l00537"></a>00537     cg0[13*5+5] = t662 * t547 + t668 * t549 + t670 * t552 / 0.2e1;
<a name="l00538"></a>00538     cg0[13*5+6] = t683 * t547 + t689 * t549 + t693 * t552;
<a name="l00539"></a>00539     cg0[13*5+7] = t715 * t547 + t721 * t549 + t725 * t552;
<a name="l00540"></a>00540     cg0[13*5+8] = t740 * t547 + t746 * t549 + t750 * t552;
<a name="l00541"></a>00541     cg0[13*5+9] = t755 * t547 / 0.2e1 + t761 * t549 + t767 * t552;
<a name="l00542"></a>00542     cg0[13*5+10] = t774 * t547 + t777 * t549 / 0.2e1 + t783 * t552;
<a name="l00543"></a>00543     cg0[13*5+11] = t790 * t547 + t796 * t549 + t798 * t552 / 0.2e1;
<a name="l00544"></a>00544     cg0[13*5+12] = t601 * t547 + t607 * t549 + t611 * t552;
<a name="l00545"></a>00545     cg0[13*6+0] = t916 * t71 + t922 * t97 + t926 * t114;
<a name="l00546"></a>00546     cg0[13*6+1] = t916 * t118 + t922 * t132 + t926 * t145;
<a name="l00547"></a>00547     cg0[13*6+2] = t916 * t149 + t922 * t155 + t926 * t164;
<a name="l00548"></a>00548     cg0[13*6+3] = t941 * t177 / 0.2e1 + t948 * t189 + t954 * t199;
<a name="l00549"></a>00549     cg0[13*6+4] = t961 * t177 + t964 * t189 / 0.2e1 + t970 * t199;
<a name="l00550"></a>00550     cg0[13*6+5] = t977 * t177 + t983 * t189 + t985 * t199 / 0.2e1;
<a name="l00551"></a>00551     cg0[13*6+6] = t994 * t177 + t1000 * t189 + t1004 * t199;
<a name="l00552"></a>00552     cg0[13*6+7] = t1013 * t177 + t1019 * t189 + t1023 * t199;
<a name="l00553"></a>00553     cg0[13*6+8] = t1039 * t177 + t1045 * t189 + t1049 * t199;
<a name="l00554"></a>00554     cg0[13*6+9] = t1054 * t177 / 0.2e1 + t1060 * t189 + t1066 * t199;
<a name="l00555"></a>00555     cg0[13*6+10] = t1073 * t177 + t1076 * t189 / 0.2e1 + t1082 * t199;
<a name="l00556"></a>00556     cg0[13*6+11] = t1089 * t177 + t1095 * t189 + t1097 * t199 / 0.2e1;
<a name="l00557"></a>00557     cg0[13*6+12] = t916 * t177 + t922 * t189 + t926 * t199;
<a name="l00558"></a>00558     cg0[13*7+0] = t916 * t428 + t922 * t430 + t926 * t436;
<a name="l00559"></a>00559     cg0[13*7+1] = t916 * t439 + t922 * t448 + t926 * t456;
<a name="l00560"></a>00560     cg0[13*7+2] = t916 * t459 + t922 * t461 + t926 * t469;
<a name="l00561"></a>00561     cg0[13*7+3] = t941 * t472 / 0.2e1 + t948 * t475 + t954 * t480;
<a name="l00562"></a>00562     cg0[13*7+4] = t961 * t472 + t964 * t475 / 0.2e1 + t970 * t480;
<a name="l00563"></a>00563     cg0[13*7+5] = t977 * t472 + t983 * t475 + t985 * t480 / 0.2e1;
<a name="l00564"></a>00564     cg0[13*7+6] = t994 * t472 + t1000 * t475 + t1004 * t480;
<a name="l00565"></a>00565     cg0[13*7+7] = t1013 * t472 + t1019 * t475 + t1023 * t480;
<a name="l00566"></a>00566     cg0[13*7+8] = t1039 * t472 + t1045 * t475 + t1049 * t480;
<a name="l00567"></a>00567     cg0[13*7+9] = t1054 * t472 / 0.2e1 + t1060 * t475 + t1066 * t480;
<a name="l00568"></a>00568     cg0[13*7+10] = t1073 * t472 + t1076 * t475 / 0.2e1 + t1082 * t480;
<a name="l00569"></a>00569     cg0[13*7+11] = t1089 * t472 + t1095 * t475 + t1097 * t480 / 0.2e1;
<a name="l00570"></a>00570     cg0[13*7+12] = t916 * t472 + t922 * t475 + t926 * t480;
<a name="l00571"></a>00571     cg0[13*8+0] = t916 * t519 + t922 * t521 + t926 * t523;
<a name="l00572"></a>00572     cg0[13*8+1] = t916 * t526 + t922 * t528 + t926 * t530;
<a name="l00573"></a>00573     cg0[13*8+2] = t916 * t533 + t922 * t535 + t926 * t544;
<a name="l00574"></a>00574     cg0[13*8+3] = t941 * t547 / 0.2e1 + t948 * t549 + t954 * t552;
<a name="l00575"></a>00575     cg0[13*8+4] = t961 * t547 + t964 * t549 / 0.2e1 + t970 * t552;
<a name="l00576"></a>00576     cg0[13*8+5] = t977 * t547 + t983 * t549 + t985 * t552 / 0.2e1;
<a name="l00577"></a>00577     cg0[13*8+6] = t994 * t547 + t1000 * t549 + t1004 * t552;
<a name="l00578"></a>00578     cg0[13*8+7] = t1013 * t547 + t1019 * t549 + t1023 * t552;
<a name="l00579"></a>00579     cg0[13*8+8] = t1039 * t547 + t1045 * t549 + t1049 * t552;
<a name="l00580"></a>00580     cg0[13*8+9] = t1054 * t547 / 0.2e1 + t1060 * t549 + t1066 * t552;
<a name="l00581"></a>00581     cg0[13*8+10] = t1073 * t547 + t1076 * t549 / 0.2e1 + t1082 * t552;
<a name="l00582"></a>00582     cg0[13*8+11] = t1089 * t547 + t1095 * t549 + t1097 * t552 / 0.2e1;
<a name="l00583"></a>00583     cg0[13*8+12] = t916 * t547 + t922 * t549 + t926 * t552;
<a name="l00584"></a>00584 }
<a name="l00585"></a>00585 
<a name="l00586"></a>00586 <span class="comment">// -- test functions -----------------------------------------------------</span>
<a name="l00587"></a>00587 <span class="comment">// 3 expresiones para la matriz de rotación, a través del exponente en so3:</span>
<a name="l00588"></a>00588 <span class="comment">// (fuente: http://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula#Conversion_to_rotation_matrix)</span>
<a name="l00589"></a>00589 <span class="comment">//      Datos intermedios:</span>
<a name="l00590"></a>00590 <span class="comment">//              const QVMatrix I = QVMatrix::identity(3),</span>
<a name="l00591"></a>00591 <span class="comment">//              const QVMatrix kkT = k.toColumnMatrix() * k.toRowMatrix(),</span>
<a name="l00592"></a>00592 <span class="comment">//              const QVMatrix k_x = k.crossProductMatrix();</span>
<a name="l00593"></a>00593 <span class="comment">//      Rotaciones:</span>
<a name="l00594"></a>00594 <span class="comment">//              const QVMatrix R1 = cos(theta)*I+ sin(theta)*k_x + (1-cos(theta))*kkT;</span>
<a name="l00595"></a>00595 <span class="comment">//              const QVMatrix R2 = I + sin(theta)*k_x + (1-cos(theta))* k_x*k_x;</span>
<a name="l00596"></a>00596 <span class="comment">//              const QVMatrix R3 = I + sin(theta)*k_x + (1-cos(theta))*(kkT-I);</span>
<a name="l00597"></a>00597 <span class="comment">//</span>
<a name="l00598"></a>00598 <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> getRotation(<span class="keyword">const</span> <span class="keywordtype">double</span> r1, <span class="keyword">const</span> <span class="keywordtype">double</span> r2, <span class="keyword">const</span> <span class="keywordtype">double</span> r3, <span class="keyword">const</span> <span class="keywordtype">double</span> Epsi)
<a name="l00599"></a>00599     {
<a name="l00600"></a>00600     <span class="keyword">const</span> <span class="keywordtype">double</span> t1 = r1 * r1;
<a name="l00601"></a>00601     <span class="keyword">const</span> <span class="keywordtype">double</span> t2 = r2 * r2;
<a name="l00602"></a>00602     <span class="keyword">const</span> <span class="keywordtype">double</span> t3 = r3 * r3;
<a name="l00603"></a>00603     <span class="keyword">const</span> <span class="keywordtype">double</span> t5 = sqrt(t1 + t2 + t3);
<a name="l00604"></a>00604     <span class="keyword">const</span> <span class="keywordtype">double</span> t6 = t5 + Epsi;
<a name="l00605"></a>00605     <span class="keyword">const</span> <span class="keywordtype">double</span> t7 = cos(t6);
<a name="l00606"></a>00606     <span class="keyword">const</span> <span class="keywordtype">double</span> t9 = t6 * t6;
<a name="l00607"></a>00607     <span class="keyword">const</span> <span class="keywordtype">double</span> t11 = (0.1e1 - t7) / t9;
<a name="l00608"></a>00608     <span class="keyword">const</span> <span class="keywordtype">double</span> t14 = sin(t6);
<a name="l00609"></a>00609     <span class="keyword">const</span> <span class="keywordtype">double</span> t16 = t14 / t6;
<a name="l00610"></a>00610     <span class="keyword">const</span> <span class="keywordtype">double</span> t17 = t16 * r3;
<a name="l00611"></a>00611     <span class="keyword">const</span> <span class="keywordtype">double</span> t19 = t11 * r1 * r2;
<a name="l00612"></a>00612     <span class="keyword">const</span> <span class="keywordtype">double</span> t21 = t16 * r2;
<a name="l00613"></a>00613     <span class="keyword">const</span> <span class="keywordtype">double</span> t23 = t11 * r1 * r3;
<a name="l00614"></a>00614     <span class="keyword">const</span> <span class="keywordtype">double</span> t28 = t16 * r1;
<a name="l00615"></a>00615     <span class="keyword">const</span> <span class="keywordtype">double</span> t30 = t11 * r2 * r3;
<a name="l00616"></a>00616 
<a name="l00617"></a>00617     <span class="keywordtype">double</span> cg[3][3];
<a name="l00618"></a>00618     cg[0][0] = t7 + t11 * t1;
<a name="l00619"></a>00619     cg[0][1] = -t17 + t19;
<a name="l00620"></a>00620     cg[0][2] = t21 + t23;
<a name="l00621"></a>00621     cg[1][0] = t17 + t19;
<a name="l00622"></a>00622     cg[1][1] = t7 + t11 * t2;
<a name="l00623"></a>00623     cg[1][2] = -t28 + t30;
<a name="l00624"></a>00624     cg[2][0] = -t21 + t23;
<a name="l00625"></a>00625     cg[2][1] = t28 + t30;
<a name="l00626"></a>00626     cg[2][2] = t7 + t11 * t3;
<a name="l00627"></a>00627 
<a name="l00628"></a>00628     <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> R(3,3);
<a name="l00629"></a>00629     <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt; 3; i++)
<a name="l00630"></a>00630         <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j = 0; j &lt; 3; j++)
<a name="l00631"></a>00631             R(i,j) = cg[i][j];
<a name="l00632"></a>00632     <span class="keywordflow">return</span> R;
<a name="l00633"></a>00633     }
<a name="l00634"></a>00634 
<a name="l00635"></a>00635 <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> so3EssentialEvaluation_bis(<span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> pose1, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> pose2)
<a name="l00636"></a>00636     {
<a name="l00637"></a>00637     <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> x;
<a name="l00638"></a>00638     x &lt;&lt; pose1;
<a name="l00639"></a>00639     x &lt;&lt; pose2;
<a name="l00640"></a>00640 
<a name="l00641"></a>00641     QuadraticFunction2 f;
<a name="l00642"></a>00642     <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> e = f(x);
<a name="l00643"></a>00643     <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> jacs2 = <a class="code" href="group__qvnumericalanalysis.html#gadd02b7275fd52c76e9cb406031b4392c" title="Estimates the Jacobian matrix for the function using the forward two-points rule...">qvEstimateJacobian</a>(f, x, 1e-6);
<a name="l00644"></a>00644     <span class="keywordflow">return</span> jacs2 | e;
<a name="l00645"></a>00645     }
<a name="l00646"></a>00646 
<a name="l00647"></a>00647 <span class="keywordtype">void</span> test_so3EssentialEvaluation()
<a name="l00648"></a>00648     {
<a name="l00649"></a>00649     <span class="comment">//#define EPSILON_LOCAL     1e-32</span>
<a name="l00650"></a>00650 
<a name="l00651"></a>00651     srand(0);
<a name="l00652"></a>00652     <a class="code" href="classQV3DPointF.html" title="3D point representation">QV3DPointF</a>  v1 = <a class="code" href="classQVVector.html#ac550cb33a94138c6a55901bc2dc23558" title="Creates a vector of random values.">QVVector::random</a>(3),
<a name="l00653"></a>00653             v2 = <a class="code" href="classQVVector.html#ac550cb33a94138c6a55901bc2dc23558" title="Creates a vector of random values.">QVVector::random</a>(3),
<a name="l00654"></a>00654             c1 = <a class="code" href="classQVVector.html#ac550cb33a94138c6a55901bc2dc23558" title="Creates a vector of random values.">QVVector::random</a>(3),
<a name="l00655"></a>00655             c2 = <a class="code" href="classQVVector.html#ac550cb33a94138c6a55901bc2dc23558" title="Creates a vector of random values.">QVVector::random</a>(3);
<a name="l00656"></a>00656 
<a name="l00657"></a>00657     <span class="comment">//const QVMatrix    R1 = expSO3(v1), R2 = expSO3(v2),</span>
<a name="l00658"></a>00658     <span class="comment">//          R1bis = getRotation(v1[0], v1[1], v1[2], EPSILON_LOCAL),</span>
<a name="l00659"></a>00659     <span class="comment">//          R2bis = getRotation(v2[0], v2[1], v2[2], EPSILON_LOCAL);</span>
<a name="l00660"></a>00660 
<a name="l00661"></a>00661     <span class="comment">//std::cout &lt;&lt; &quot;R1 = &quot; &lt;&lt; R1 &lt;&lt; std::endl;</span>
<a name="l00662"></a>00662     <span class="comment">//std::cout &lt;&lt; &quot;R1bis = &quot; &lt;&lt; R1bis &lt;&lt; std::endl;</span>
<a name="l00663"></a>00663     <span class="comment">//std::cout &lt;&lt; &quot;R2 = &quot; &lt;&lt; R2 &lt;&lt; std::endl;</span>
<a name="l00664"></a>00664     <span class="comment">//std::cout &lt;&lt; &quot;R2bis = &quot; &lt;&lt; R2bis &lt;&lt; std::endl;</span>
<a name="l00665"></a>00665 
<a name="l00666"></a>00666     <span class="comment">// E = R2.CrossProductMatrix( (c2-c1) / Norm2(c2-c1)).Transpose(R1):</span>
<a name="l00667"></a>00667     <span class="comment">//const QVMatrix E = R2 * ( (c2-c1) / (c2-c1).norm2() ).crossProductMatrix() * R1.transpose();</span>
<a name="l00668"></a>00668 
<a name="l00669"></a>00669     <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> pose1, pose2;
<a name="l00670"></a>00670     pose1 &lt;&lt; v1;
<a name="l00671"></a>00671     pose1 &lt;&lt; c1;
<a name="l00672"></a>00672 
<a name="l00673"></a>00673     pose2 &lt;&lt; v2;
<a name="l00674"></a>00674     pose2 &lt;&lt; c2;
<a name="l00675"></a>00675 
<a name="l00676"></a>00676     <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> jacs(9,13);
<a name="l00677"></a>00677     so3EssentialEvaluation(pose1.data(), pose2.data(), jacs.getWriteData());
<a name="l00678"></a>00678 
<a name="l00679"></a>00679     <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> jacs2 = so3EssentialEvaluation_bis(pose1, pose2);
<a name="l00680"></a>00680     <span class="comment">//QVVector x;</span>
<a name="l00681"></a>00681     <span class="comment">//x &lt;&lt; v1;</span>
<a name="l00682"></a>00682     <span class="comment">//x &lt;&lt; c1;</span>
<a name="l00683"></a>00683     <span class="comment">//x &lt;&lt; v2;</span>
<a name="l00684"></a>00684     <span class="comment">//x &lt;&lt; c2;</span>
<a name="l00685"></a>00685 
<a name="l00686"></a>00686     <span class="comment">//QuadraticFunction2 f;</span>
<a name="l00687"></a>00687     <span class="comment">//const QVVector e = f(x);</span>
<a name="l00688"></a>00688     <span class="comment">//const QVMatrix jacs2 = qvEstimateJacobian(f, x, 1e-6);</span>
<a name="l00689"></a>00689 
<a name="l00690"></a>00690     <span class="comment">//std::cout &lt;&lt; &quot;E = &quot; &lt;&lt; QVVector(9, E.getReadData()) &lt;&lt; std::endl;</span>
<a name="l00691"></a>00691     <span class="comment">//std::cout &lt;&lt; &quot;e1 = &quot; &lt;&lt; jacs.getCol(12) &lt;&lt; std::endl;</span>
<a name="l00692"></a>00692     <span class="comment">//std::cout &lt;&lt; &quot;e2 = &quot; &lt;&lt; e &lt;&lt; std::endl;</span>
<a name="l00693"></a>00693 
<a name="l00694"></a>00694     <span class="comment">//std::cout &lt;&lt; &quot;jacs 1 = &quot; &lt;&lt; jacs &lt;&lt; std::endl;</span>
<a name="l00695"></a>00695     <span class="comment">//std::cout &lt;&lt; &quot;jacs 2 = &quot; &lt;&lt; jacs2 &lt;&lt; std::endl;</span>
<a name="l00696"></a>00696     std::cout &lt;&lt; <span class="stringliteral">&quot;||jacs1 - jacs2|| = &quot;</span> &lt;&lt; (jacs - jacs2).norm2() / ( jacs.norm2() + jacs2.norm2() )&lt;&lt; std::endl;
<a name="l00697"></a>00697     }
<a name="l00698"></a>00698 
<a name="l00699"></a>00699 
</pre></div></div>
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